How big is this thing going to be? You realize that IMAX is about 4k and that's a huge screen. Billboards are printed at about 5-10 lines per inch which normally equates to around 10-20 Pixels Per Inch. At five feet distance, 100 Pixels per Inch is more than enough detail. We've done all kinds of poster work, from brochures to huge murals, and you only need the high resolution output on stuff that's actually going to be handled - brochures, flyers, magazines - because that's the stuff that will be looked at most closely. Posters tend to be printed at 133LPI screens - about 260 Pixels Per Inch if you follow Adobe's guidelines - or in that range. Larger stuff is done with lower LPI screens for two reasons. The first goes back to the old days of huge process cameras. To get the dot structure into an image so if can be printed, the image is photographed on lith film (extremely high contrast, it's black or clear. No greys).
A sheet of film, called a magenta screen, is placed over the negative. This magenta screen (about $50 for a sheet that's 8x10) is, as you might have guessed, magenta in color, and has the halftone dot structure on it, but the dots are fuzzy. As more light passes through a clear area onto film, and effect called bloom or spread, happens, and the dot that actually gets burned into the file gets larger. Less light - smaller dot. Now, the higher the Lines Per Inch count is, the smaller the dots on the screen and the harder they are to make, and thus, they're more expensive. I've seen screens up to 150 Lines Per Inch (halftone screens are meansured in lines of dots per inch), but the common range for hand-held material is between 85 and 133 - 85 (and sometimes lower, like 60) is used for newspapers, while the higher stuff is reserved for magazines and other presentation material where quality is important.
Now, when taking original artwork (photographs, paintings, anything that hasn't been screened yet) and photographing it through a process camera to make the negatives that make the plates that you print with, you have no choise but to use a sheet of film that's the same size as your output. Usually this tops off at about 24 inches wide, but it can be more. Length can be 8 feet or more since film this large is stored in rolls, just like the paper you'll be printing. Getting a magenta screen that large that's 150LPI is going to be VERY expensive, and since these are very susceptible to scratches, and handling a sheet that large isn't the most elegant thing a person can do, well, you see the problem. A scratched screen means every image you shoot through it will be degraded.
Combine this with the fact that you're gong to be viewing the poster/bilboard/mural from several feet away, and that tiny dots at that distance will be virtually indistringuishable (they're hard enough to see at 100DPI up close - Mac monitors are 72 DPI and look great), there's not really much point in investing in such an expesive, unnecessary piece of equipment that is so easily damaged.
The same is true of the plates. Ultraviolet light is shone though the film negative onto an emulsion that coats the plates. Where the light hits, the emulsion is changed to a permanent coating. The rest is washed off. ink is then picked up by the emulsion and transferred to a roller and then onto the paper. Again, a small scratch will leave a mark in the final print. And finer detail, especially on such a large surface area, is much more susceptible to damage. Larger dots can withstand more damage than smaller dots, and again, for large output, there's not that much point in dealing with such small dot structures.
Now, zip into this decade, where Process Photography is a rarity. Digital files still need to be turned into halftones, and image setters do this for us. They can burn the image to paper, film or even directly to the plates themselves. But the final output is still dots pressed to paper. Except in small runs, where the image is output on a a large printer, usually thermal wax transfer, dye sublimation, or inkjet. These have fixed resolutions, measured in Dots Per Inch (NOT to be confused with Pixels per Inch). They use multiple dots and dithering routines to apply enough ink of each color to create the right color for any pixel in the image they're printing. These seem to max out at around the 1200DPI range (far short of the 24000 DPI that some image setters were capable of, but those had to be able to draw halftone dots at very exact sizes), though they can interpolate higher resolutions by rolling the paper through in smaller increments (thus you see dual resolutions like 1200x2400 - 1200 physical dots, and by rolling the paper through at half dot increments, it can double the vertical resolution). These need a certain number of physical dots to be able to reproduce the color of any pixel in an image, so your image should have fewer pixels per inch on output than the printer has dots per inch. You CAN print an image at 1200 pixels per inch on a 1200DPI printer, but you won't get get a pixel per pixel copy. You have to give the printer room to rebuild the pixels. 8 or more dots to a pixel is good, though I have yet to hear any solid rules on this. The larger the image resolution, the longer it will take to print though, and since time is money in print bureaus...
Most billboards up until recently were shot on 35mm film. That film, depending on the actual stock, has a resolution of about 30-40 lines per millimeter (color is lower than black & white). That's about 1400 lines. Double that for an accurate pixel count, and you get 2800 pixels. Actually a touch more since 35mm isn't the true width of the image - it's slightly wider - figure about 3k at the most. That's more than good enough for billboards.
Now, getting back to the Mac monitors, at 72DPI... Look at one from five feet away. Is it sharp? Does it look ok? I'd hope so since people normally work much closer to these and they don't seem to say, gee, this thing is so blocky! I see all the dots and the image is crap!
Well, I think you just found a half decent output resolution for a mural that you'll be seeing from five feet.
Something else to consider before tackling something like this...
In Photoshop, I created a 30Kx30K image. Instantly a 2.9GB swapfile was created. I made a gradient. Something simple that is normally done so fast I never notice any time spent on it. The gradient process took over six minutes to complete! TWELVE minutes passed from the time I started the gradient to the time that Photoshop finally finished refreshing the image. Yikes! That was just for a single operation. I wasn't doing anything fancy.
Now, saving the image as a .psd took 11 minutes, 53 seconds, only to get an error message that the file could not be saved because it exceeded the 2.00 GB limit for Photoshop files. That wasn't fun. So, I tried another format. Why not? I couldn't save the layers so they're toast. I tried JPEG. Nope! I couldn't save the image as a JPEG with the optimized baseline setting because there wasn't enough RAM. Umm.. I have 2 GB! Ok, fine I'll change it. Normal baseline mode took 4 minutes. Finally. Loading that image took 2:20. Yawn.
Now imagine how long actually rendering anything at 30k would take. That's a lot more to do than just making a gradient. Figure if a gradient operation, that take less than second at normal resolutions takes 6 minutes - over 360 times longer, the surely you can expect pretty much any other type of operation to have the same kind of hit on performance. A typical render in Lightwave takes about ten minutes to a couple hours. Lets take a 20 minute render for example, and bump that up by 360... 7200 minutes. That's 120 hours. That's like a workweek at Warner Brothers!
Five continuous days, assuming you don't ever do anythng else with the machine that could slow it down. And that it doesn't crash... And the power doesn't go out...
No, there's no reason to render at 30k for print. That's just insane.
. thanks for the additional info